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Holonomicity from a Heegaard-Floer Perspective

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arxiv 2501.01519 v2 pith:ANSA45AN submitted 2025-01-02 math.GT

Benjamin Cooper , Robert Deyeso III This is my paper · ORCID
classification math.GT
keywords coloredholonomicitypolynomialsalexanderanalogyassociatedcategorifiedcharacteristic
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abstract

We construct $S^r$-colored knot Floer homologies and prove that they satisfy categorified recurrence relations. The associated Euler characteristic implies $q$-holonomicity of the corresponding sequence of colored Alexander polynomials, in analogy with the AJ conjecture for colored Jones polynomials.

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  1. Colored knot Floer homology: structures and examples

    math.GT 2025-08 conditional novelty 7.0 of 10

    The authors construct an n-colored knot Floer homology as a colimit over cable links with increasing full twists and equip it with a module structure over an explicit algebra.

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